#### Answer

The mug does not slide.

#### Work Step by Step

We can find the maximum possible magnitude of acceleration of the mug which can be provided by the force of static friction.
$F_f = ma$
$mg~\mu_s = ma$
$a = g~\mu_s$
$a = (9.80~m/s^2)(0.50)$
$a = 4.90~m/s^2$
We can find the deceleration of the car during the braking period.
$a = \frac{v^2-v_0^2}{2x}$
$a = \frac{0-(20~m/s)^2}{(2)(50~m)}$
$a = -4.0~m/s^2$
Since the mug's maximum possible magnitude of acceleration provided by the force of static friction is greater than the magnitude of deceleration of the car, the mug does not slide.